67584 has 48 divisors (see below), whose sum is σ = 196560. Its totient is φ = 20480.

The previous prime is 67579. The next prime is 67589. The reversal of 67584 is 48576.

It is a happy number.

67584 is nontrivially palindromic in base 5.

It is an interprime number because it is at equal distance from previous prime (67579) and next prime (67589).

It is a tau number, because it is divible by the number of its divisors (48).

Its product of digits (6720) is a multiple of the sum of its prime divisors (16).

It is not an unprimeable number, because it can be changed into a prime (67589) by changing a digit.

67584 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (2) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 6139 + ... + 6149.

It is an arithmetic number, because the mean of its divisors is an integer number (4095).

2⁶⁷⁵⁸⁴ is an apocalyptic number.

67584 is a gapful number since it is divisible by the number (64) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 67584, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (98280).

67584 is an abundant number, since it is smaller than the sum of its proper divisors (128976).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

67584 is a wasteful number, since it uses less digits than its factorization.

67584 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 36 (or 16 counting only the distinct ones).

The product of its digits is 6720, while the sum is 30.

The square root of 67584 is about 259.9692289484. The cubic root of 67584 is about 40.7331469573.

The spelling of 67584 in words is "sixty-seven thousand, five hundred eighty-four".